Sudakov-Logarithmen in der elektroschwachen Wechselwirkung

Experiments at the future colliders LHC and ILC will, for the first time, explore electroweak reactions at energies in the TeV region, i.e. far beyond the masses of the W and Z bosons. In exclusive processes without the emission of massive gauge bosons double-logarithmic contributions, so-called Sudakov logarithms, will then become relevant. Precise theoretical predictions require the knowledge of the complete logarithmic two-loop corrections in the high energy limit, thus exceeding the approximation through the leading powers of logarithms known so far. This PhD thesis is focussed on the calculation of analytic two-loop corrections to the form factor of an Abelian vector current. It also studies with the help of evolution equations the consequences of these results for electroweak cross sections of four-fermion processes. Contributions from the Higgs boson and the mass difference between the W and the Z boson are considered as well, and the factorization of the singular contributions from the massless photon is demonstrated. The results represent theoretical two-loop predictions for four-fermion processes in the accuracy needed for the precision experiments at the ILC.